Part 1: The SI System and Base Units
The SI system rests on seven base quantities that are defined independently of each other. Length is measured in metres, mass in kilograms, time in seconds, electric current in amperes, temperature in kelvins, amount of substance in moles, and luminous intensity in candelas. All other units — newtons, joules, pascals, watts, and so on — are derived by algebraic combination of these seven. The choice of base units is conventional: what matters is that the set is both complete (can express all physical quantities) and minimal (no base unit can be derived from the others).
Part 2: Dimensional Formulas of Key Derived Quantities
Every derived unit has a unique dimensional formula. The most important for NEET are: Force [M^{1}$$L^{1}$$T^{-2}], Energy/Work/Torque [M^{1}$$L^{2}$$T^{-2}], Power [M^{1}$$L^{2}$$T^{-3}], Pressure/Stress/Young's modulus [M^{1}$$L^{-1}$$T^{-2}], Momentum [M^{1}$$L^{1}$$T^{-1}], Angular momentum [M^{1}$$L^{2}$$T^{-1}], Surface tension [M^{1}$$L^{0}$$T^{-2}], and Viscosity [M^{1}$$L^{-1}$$T^{-1}]. NEET frequently asks which pair of quantities shares the same dimensional formula — for example, torque and energy both have [M^{1}$$L^{2}$$T^{-2}], while pressure and energy density both have [M^{1}$$L^{-1}$$T^{-2}].
Part 3: Dimensional Analysis — Uses and Limitations
Dimensional analysis exploits the principle that every valid physical equation must be dimensionally homogeneous. Its three uses are: (1) checking equation validity by verifying both sides carry identical dimensions; (2) deriving functional relationships by setting up a power law and solving simultaneous equations for the exponents; (3) converting numerical values between unit systems using the base-unit substitution formula. Its two limitations are the inability to determine dimensionless constants and the inability to discriminate between physically distinct formulas that share the same dimensions.
Part 4: Significant Figures
Significant figures encode the precision of a measurement in the written number itself. The key rules: leading zeros are never significant (0.0046 has 2 sig figs); trailing zeros after the decimal point are always significant (4.600 has 4 sig figs); in scientific notation, all digits in the coefficient are significant ( has 3 sig figs). For calculation: addition/subtraction — round to the fewest decimal places among the terms; multiplication/division — round to the fewest significant figures among the factors.
Part 5: Classification of Errors
Errors divide into systematic and random. Systematic errors have a consistent direction and magnitude — zero error in a vernier caliper, incorrectly calibrated weights, observer's consistent bias in reading a meniscus. They affect accuracy (closeness to true value) but not precision (closeness of repeated readings to each other). Random errors are irregular — they affect precision. Their effect is quantified via the mean and mean absolute deviation. The limiting factor in any measurement is its least count — the smallest division readable on the instrument.
Part 6: Error Propagation
The rules for combining errors in derived quantities are essential for NEET numericals. For sums and differences, always add absolute errors (even for subtraction). For products and quotients, always add relative errors. For a quantity raised to a power, multiply the relative error by the exponent's magnitude. For a formula like Z = BC / , the percentage error is 2(%A) + 1(%B) + 1(%C) + 3(%D). These rules guarantee the maximum possible error in the derived quantity — they represent a conservative (worst-case) bound.